nonlinear
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1: Peter A. Clarkson
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►His well-known book Solitons, Nonlinear Evolution Equations and Inverse Scattering (with M.
…He is also coauthor of the book From Nonlinearity to Coherence: Universal Features of Nonlinear Behaviour in Many-Body Physics (with J.
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2: Mark J. Ablowitz
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►Ablowitz is an applied mathematician who is interested in solutions of nonlinear wave equations.
Certain nonlinear equations are special; e.
…Some of the relationships between IST and Painlevé equations are discussed in two books: Solitons and the Inverse Scattering Transform and Solitons, Nonlinear Evolution Equations and Inverse Scattering.
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3: Bernard Deconinck
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►Deconinck is interested in nonlinear waves.
He has worked on integrable systems, algorithms for computations with Riemann surfaces, Bose-Einstein condensates, and methods to investigate the stability of solutions of nonlinear wave equations.
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4: Sidebar 22.SB1: Decay of a Soliton in a Bose–Einstein Condensate
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►Jacobian elliptic functions arise as solutions to certain nonlinear Schrödinger equations, which model many types of wave propagation phenomena.
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5: Alexander A. Its
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► Novokshënov), published by Springer in 1986, Algebro-geometric Approach to Nonlinear Integrable Problems (with E.
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6: Alexander I. Bobenko
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►Bobenko’s books are Algebro-geometric Approach to Nonlinear Integrable Problems (with E.
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7: 23.21 Physical Applications
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§23.21(ii) Nonlinear Evolution Equations
►Airault et al. (1977) applies the function to an integrable classical many-body problem, and relates the solutions to nonlinear partial differential equations. …8: 29.19 Physical Applications
9: 9.16 Physical Applications
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►Within classical physics, they appear prominently in physical optics, electromagnetism, radiative transfer, fluid mechanics, and nonlinear wave propagation.
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►Airy functions play a prominent role in problems defined by nonlinear wave equations.
These first appeared in connection with the equation governing the evolution of long shallow water waves of permanent form, generally called solitons, and are predicted by the Korteweg–de Vries (KdV) equation (a third-order nonlinear partial differential equation).
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